To further study the proposed method, we analyze its behavior as the number of layers \(K\)  grows.
Intuitively, since the optimal power allocation is a fixed point of the classical WMMSE iteration [1]}, one would expect deeper layers of the UWMMSE to more closely resemble its classical counterpart.
To formalize this intuition, let us introduce the following notation.
For any given channel state \({\mathbf {H}}\) , let us define the optimal power allocation, i.e., the solution to (REF ), as \({\mathbf {p}}^*\) .
Accordingly, we define \(v_i^* = \sqrt{p_i^*}\) , \(u_i^*\)  as given by () when \({\mathbf {v}}^{(k-1)}\)  is replaced by \({\mathbf {v}}^*\) , and \(w_i^* = (u_i^* h_{ii} v_i^*)^{-1}\) .
Also, for simplicity we consider the case where \({\mathbf {a}}^{(k)} = \mathbf {1}\)  for all \(k\)  and study the convergence of \({\mathbf {b}}^{(k)}\) .
With this notation in place, the following result can be shown.
